1.4.1 Excited-State Geometries
The excitation of an electron from a bonding orbital into a nonbonding or antibonding orbital changes the bonding situation and thus the equilibrium geometry of the molecule as well. The larger the differences in the bonding or antibonding contributions to individual bonds that are provided by the electrons located in the orbitals occupied before and after the transition, the more pronounced will be the geometry changes. Hence, for extended a sys- tems with strongly and fairly uniformly delocalized a orbitals, only small bond-length changes are to be expected. Steric and electronic effects are frequently very delicately balanced, so it is mainly the dihedral angles that differ appreciably in the different electronic states of the molecule. (Cf. Ex- ample 1.13.)
The experimental determination of the structure of molecules in excited states is difficult. For small molecules accurate data may be obtained from the moments of inertia determined from the rotational fine structure in the electronic spectra. (Cf. Section 1.3.6.) Structural data for formaldehyde in the ground and the lowest excited singlet and triplet states are collected in
- Table 1.4. For larger molecules the necessary information may be retrieved from Franck-Condon factors if a sufficient number of progressions corre- sponding to the various normal modes of vibration show up in the UV spec- trum. The first Franck-Condon analysis for a larger molecule showed that the So + S, transition in benzene is accompanied by a CC bond-length change of AR = 3.7 pm and a very small contraction of the CH bonds (AR = - 1 pm) (Craig, 1950). Similar results were obtained for naphthalene (Figure 1.19). Since only (AR)2 can be derived from the spectra, supplemen- tary experimental information or theoretical data are needed to determine the sign of the bond-length change.
Most data for geometries of excited states stem from theoretical argu- ments or calculations. Qualitative concepts such as the Walsh rules (cf.
Buenker and Peyerimhoff, 1974) have proven very useful. Another valuable
Table 1.4 Excited-State Geometries, all Distances in pm
C H S H '
so s I T, S" s I T,
Rco 120.8 132.1 130 RM 120 131.7 135.6
RCH 1 1 1.6 109.2 1 1 1 QHCC 180" 130.5" 128.0"
QHCO 116.5" 121.5" 116" (trans) (cis) (P" 0.0 21" 36"
Johnson et al.. 1972.
Jobetal., 1%9.
Winkelhofer et al.. 1983.
Deviation from planarity.
rule was proposed by Imamura and Hoffmann (1968) for situations in which two a systems, each with q a electrons, are connected by a formal single bond. If q = 4n + 2, as in biphenyl (3), a twisted ground state and a planar excited state are predicted. If q = 4n both the ground state and the excited state are predicted to be planar. If q is odd, the ground state should be planar and the excited state twisted.
Initial estimates of geometry changes on excitation of a systems may be obtained from the linear relation
between the a bond order p,, and bond distance R,,. Using this relationship, very satisfactory results for the geometry changes for the excitation of naph- thalene are obtained even from HMO calculations. A symmetry-based pro- cedure for the determination of molecular geometry changes following elec- tronic excitation has been proposed by Bachler and Polanski (1990).
Figure 1.19. Bond-length changes of naphthalene (pm) on 310-nm excitation (adapted from Innes, 1975).
Ab initio calculations on small molecules give very detailed information.
Thus, acetylene is calculated to be bent into a trans configuration in the lowest singlet state and into a cis configuration in the lowest triplet state.
(Cf. Table 1.4.) Hexatriene (4) was shown to have three minima of compa- rable energy in the T, state, one planar and two at geometries twisted by 90"
around the central o r the terminal double bond. For longer polyenes, twist- ing around the central double bond is to be expected (BonatiC-Koutecky and Ishimura, 1977). l k i s t e d excited states of n systems play a very important role in many photochemical reactions and will be discussed in detail in Sec-
tion 7.1.
Example 1.13:
In many cases a combination of force-field methods and semiempirical calcu- lations in the n approximation has proven very useful for calculating geome-
Absorption Fluorescence
I I
So geometry S, geometry (8 = 50") ( 0 = 32')
Absorption Fluorescence
28
So geometry s, %-
S1 geometry 10 = 23') l 0 = 1 " )
Figure 1.20. Electronic singlet term system for I- and 2-phenylnaphthalene calculated for ground and excited-state geometries. The weakly allowed char- acter of transitions between the ground state and the IL,, state is indicated by broken arrows (by permission from Gustav et al., 1980).
1.4 PKOPEKI'IES OF MOLECULES IN EXCITED STATES 47
tries of excited states (Gustav and Sikhnel, 1980). Along these lines it was shown that in going from So to S, the torsional angle between naphthalene and the phenyl group in I-phenylnaphthalene (5) changes from 50" to 32" and in 2-phenylnaphthalene from 23" to a value close to 0'. From Figure 1.20 it can be seen that calculations for these optimized excited-state geometries lead to an interchange of the first two excited states of 5 compared to the order cal- culated for the ground-state geometry. As a consequence the vertical fluores- cence from S, is strongly allowed for the 1-phenyl derivative but only weakly allowed for the 2-phenyl derivative, as is the vertical absorption into S, for both molecules. This explains the difference in the fluorescence lifetimes of t J S , ) = 35 ns (5) and t,(S,) = 438 ns (6) observed for these two compounds (Gustav et al., 1980).
1.4.2 Dipole Moments of Excited-State Molecules
Molecules in a n electronically excited state have chemical and physical properties that differ from those of ground-state molecules. As a result of
Table 1.5 Dipole Moments of Ground and Excited States, all Values in D, Calculated Data in Parentheses
--
State
Molecule SO TI s I Sr Ref.
Buckingham et al., 1970.
Hochstrasser and Noe. 1971.
Labhart. 1%6.
" Taylor, 1971.
Rischof et at.. 1985.
48 1 SPECTROSCOPY IN THE VISIBLE AND UV REGIONS
1.4 PROPERTIES OF MOLECULES IN EXCITED STATES 49
excitation, the electron distribution changes, and the dipole moment may as well. This is often apparent from the solvent dependence of absorption and luminescence (cf. Section 2.7.2 and Section 5.5.3) as well as from the chem- ical properties of the molecule, such as basicity and acidity.
In Table 1.5 some data for ground- and excited-state dipole moments are collected. The n+n* excitation of carbonyl compounds is accompanied by a charge shift from the electronegative oxygen atom into the delocalized n*
orbital, and the dipole moments of the T, and the S, states are smaller than those of the ground state. The lowest excited states of molecules with donor and acceptor groups on the n system often exhibit intramolecular charge transfer from the donor to the n system and to the acceptor or from the n system to the acceptor. As a consequence, the excited-state dipole moment is often much higher than the ground-state value. Particularly large changes of the dipole moment are to be expected for exciplexes, since a pronounced charge transfer is characteristic for their excited states. (Cf. Section 2.6 and Section 5.4.3.) Finally, the so-called TICT states (twisted internal charge transfer, cf. Section 4.3.3) exhibit large dipole moments.
In solution, even centrosymmetric molecules can have large dipole mo- ments in the excited state, as was first demonstrated in the case of 9,9'- bianthryl (7) (Beens and Weller, 1968). The symmetrical compound 8 is an example in which electronic excitation is localized almost entirely in one of the polar aromatic end groups, due to solvent-induced local site perturbation (Liptay et al., 1988a). In solution, polyenes may also show unsymmetrical charge distributions with nonvanishing dipole moments (Liptay et al., 1988b;
see also Section 2.1.2).
1.4.3 Acidity and Basicity of Molecules in Excited States Changes in the electron distribution on excitation are connected with changes in basicity and acidity. This becomes evident if one considers the indicator equilibrium
For the base B to act as an indicator it must absorb at a different frequency after protonation. Suppose that the excitation energy into the lowest singlet state 'AE = E(Sl) - E(So) or into the lowest triplet state 'AE = E(Tl) -
E(So) is higher for BHo than for B. Imagine a solution of pH equal to the ground-state pK, so that [B] = [BHO]. On excitation BH@ will find itself at a higher energy than excited B and will exhibit a strong tendency to change
to B. Thus, it will become a stronger acid. If B absorbs at higher frequency than BH@, then B will become a stronger base on excitation. Whether a proton transfer in the excited state will actually take place depends on its lifetime and on the presence of barriers in the excited potential energy sur- face.
The relationship between the excitation energy change upon protonation and the change in equilibrium constant upon excitation is formalized in the Farster cycle (Forster, 1950), which is illustrated in Figure 1.21. Proceeding from the ground state BHo to excited B* + H@ by two different routes yields the equality
NLhvBHo + AH* = NLhvB + AH (1.52)
AH* - AH = NL(hvB - hvHBO)
where AH and AH* are the enthalpy changes in the ground and excited states, respectively, and NL is the Avogadro number. If in dilute solutions AH can be approximated by the standard value AH, and if entropy effects may be neglected, Equation (1 32) yields, using AGO = - RTlnK = - 2.303 RTpK
N L ( ~ ~ B - hvBHo) " AAHo ;= &AGO .z 2.303 RTApK
When numerical values for constants are inserted, the following relation be- tween the change in the pK value and the shift A5 of the absorption maxi-
Figure 1.21. The Firrster cycle. A E and AE' refer to the excitation energies and AH and AH* to the reaction enthalpies corresponding to the equilibrium BH@ = B +
H@ in the ground and excited state, respectively.
4
AE
AE'
- - - - - I t - - - - . - 1.1
BH@ - K B + H@
50 1 SPECTROSCOPY IN THE VISIBLE AND UV REGIONS 1.4 PROPERTIES OF MOLECULES IN EXCITED STATES 5 1
mum for the lowest singlet or triplet transition due to protonation is obtained for T = 298 K:
ApK = 0.00209 (5, - GBHo)/crn-' (1.53)
Near 300 nm a spectral shift of 30 nm corresponds approximately to a change in wave number of A 5 = 3,300 cm-I. From Equation (1 53) this results in a pK value change of 7 units. Since shifts of this extent are quite common on protonation, changes in dissociation constants of protonated compounds by 6-10 orders of magnitude on excitation are often observed.
Depending on whether the change in ApK is negative or positive, i.e. de- pending on whether the pK value of the excited state is smaller or larger than that of the ground state, the excited-state species will be a stronger acid (the conjugate base will be weaker) or a stronger base (the conjugate acid will be weaker). Molecules with acidic substituents that are electron donors, such as 1-naphthol (9) with pK(So) = 9.2 and pK(SI) = 2.0 (Weller, 1958) are more acidic in the excited singlet state. Molecules with acidic substi- tuents that are electron acceptors, such as naphthalene-1-carbocylic acid (10) with pK(So) = 3.7 and pK(S,) = 10.0 (Watkins, 1972), are less acidic in the excited singlet state. This is due to the generally much larger degree of charge transfer between the substituent and the parent n system in the ex- cited singlet. For the same reason, a molecule with a basic electron-donor substituent, such as aniline, becomes much less basic in the excited singlet state.
Of special interest are compounds such as 3-hydroxyquinoline (11) for which it is expected that the heterocyclic nitrogen becomes more basic in the excited state whereas the hydroxyl group should become more acidic.
Scheme 1
As a consequence, different ionization sequences can be obtained in the So and S, states, as illustrated in Scheme 1 (Mason et a]., 1968).
At the extremes of the acidity range studied, the cation and the anion are the species found in both the ground and S, states. At intermediate pH val- ues, the hydroxy tautomer of the neutral molecule is the predominant spe- cies in the ground state. On excitation, however, the phenolic group be- comes more acidic and the nitrogen more basic. The zwitterion is more stable, and only the fluorescence of this species is observed.
Excitation into the TI state changes the pK yalue in the same direction as excitation into the S, state, but much less, and the pK(Tl) value tends to be closer to pK(So) than to pK(Sl):
The trends are easy to understand in qualitative terms. For instance, acidic and basic substituents that are n-electron donors, such as OH and NH,, become more acidic and less basic in the excited state, respectively. The ability of the substituent to transfer electron density into the arene is greatly increased upon excitation, since it then can occur into one of the bonding orbitals that were doubly occupied in the ground state. (Cf. Section 2.4.2.) The increased positive charge on the substituent functionality increases its acidity and reduces its basicity.
In order to understand the striking difference between the S, and TI states, one needs to go beyond a simple consideration of the charge densities (Constanciel, 1972). From the FOrster cycle shown in Figure 1.21 it is clear that the critical quantity is the difference in the substituent effect on the
Figure 1.22. Schematic representation of the energy levels for a case in which the lowest excited states T, and S, originate from a n-n* excitation in the protonated species. and from a w n * excitation in the nonprotonated species, with a corre- spondingly smaller singlet-triplet splitting E ( S , ) - E(T,).
52 1 SPECTROSCOPY IN THE VISIBLE AND W REGIONS 1.5 QUANTUM CHEMICAL CALCULATIONS OF ELECTRONIC EXCITATION 53 singlet versus the triplet excitation energy. Differences are to be expected,
since in simple arenes such as benzene and naphthalene the two states orig- inate in different kinds of configurations, S, being of the L, and TI of the La type. (See Section 2.2.) Also, with increasing charge-transfer contributions to an excited state, the orbital @, out of which excitation occurs tends to separate in space from the orbital c$~ into which it occurs, and their exchange integral K,, tends to decrease. (Cf. Section 1.3.2.) Upon protonation, the charge-transfer nature of the excited states is greatly decreased and Kik in- creases. Equations (1.23) and (1.24) show that the energy of the singlet but not the triplet excited configuration increases as a result. This is reflected in the state energies, making protonation of the S, species less advantageous (aniline) or its deprotonation more advantageous (phenol).
Xanthone (12) and several substituted benzophenones (13) have pK(Tl) values lying outside the range defined by pK(So) and pK(Sl) (Ireland and Wyatt, 1973). In these molecules the lowest excited state is a (n, n*) state in the ketone and a (n, n*) state in its conjugate acid. Since the S,-TI energy difference is much smaller for (n, n*) states than for (n, n*) states, molecules of this type, which are already stronger bases in the S, than in the So state, can become even stronger bases in the T, state. The relative energies of the states are shown schematically in Figure 1.22. The pK order is therefore PK(S& < PK(SI) < PK(T,)-